Research Plan Outline

Guy Ron 1

Lawrence Berkeley National Lab

1 Introduction

This research plan presents two avenues of research which will be followed by the proposedexperimental group.

Medium energy electronuclear physics, namely nucleon structure studies, in which sig-nificant results have already been achieved will comprise the bulk of the research effort.One such experimental proposal is already scheduled and preparation for the experimentwill strengthen the (medium-energy) electronuclear experimental group at TAU (Profs.Piasetzky and Lichtenstadt). At least one additional high-impact experimental proposalis already planned and will be submitted in the near future. Collaboration with leadingexperimental (TAU, JLab, Rutgers, SMU, USC) and theoretical (HUJI, UW) groups iswell established. While the focus of this research is currently centered around the accessi-ble JLab facility, an obvious extension of the research is with the inception on the plannedElectron-Ion Collider (EIC) which will allow measurement at experimental regimes notcurrently available in any medium-energy facility. This part of the research represents anatural continuation to the long and highly successful studies of the strong interaction andstrongly interacting hadronic matter by the Tel Aviv University nuclear physics experi-mental group. This low to medium energy research complements the high energy studiesled by the Tel Aviv University high energy experimental physics groups.

The second venue of research will focus on standard model tests using rare isotopes (pro-duced in accelerators), with an envisioned offline development lab at TAU and at leastone onsite experimental location. With the advent of the new SARAF facility, such exper-iments which may then be performed in Israel will be able to produce results competitivewith the best results from other locations. Collaboration with leading experimental groupshas already been initiated (namely LBL, WI, ANL) and is expected to continue.

Modus Operandi

Both venues of research outlined below require the use of large scale facilities, unavailableonsite at the Tel Aviv University. Thus, a large fraction of the research will be conducted,

1 Guy Ron, GRon@lbl.gov

Research Proposal Outline 28 September 2009

both by the PI and by graduate students in the experimental group, at offsite locations.It is likely that these locations will include:

• The SARAF experimental facility (see 5).• The Lawrence Berkeley National Lab.• Argonne National Lab.• University of Washington - Center for Experimental Nuclear Physics and Astrophysics

(CENPA).• The Thomas Jefferson National Accelerator Facility (JLab).

Research in offsite locations will include the setup and running of the experiments and willcoincide with available resources at these locations (for example, with available beam-timeat the accelerator sites).

Although the actual experiments are to be conducted off-site, much of the design andpreparation for the experiments will be done in a lab which will be set up at the TelAviv University. This lab will focus on the laser trapping and manipulation of atoms, andwill develop the necessary tools for the experiments using stable (or long lived) isotopes(it would be advantageous to have the option of testing the designs using rare isotopes,which will require a lab configuration which allows the safe use and storage of long livedradioactive isotopes).

Another onsite activity will be the investigation and optimization of detector designs foruse in both types of experiments. This lab will be equipped with standard electronicworkbenches to allow testing and construction of standard detector components (suchas photomultipliers, scintillators, strip detectors, etc.). For non-standard detector design(sometimes requiring cleanroom assembly and microfabrication) we will collaborate withthe detector development group at the Weizmann Institute, which may extend to M.Sc.students (or early stage PhD student) from TAU taking part in the actual detector con-struction and testing at WI (similar to the Tel Aviv LHC exprimental efforts). Detectordesigns for the electronuclear physics research will be studied in collaboration with othernuclear physics groups (eg. JLab, Kent State U., and Rutgers U.), with prototype con-struction at both TAU and JLab.

Finally, simulations and analysis of the experiments (for both research topics) will beconducted on site, using dedicated computers. Practically all experimental physics groupsin Israel make use of the same experimental tools (namely, ROOT, GEANT, and SIMION).Sadly, very little information is shared between these groups. We envision creating aknowledge repository for the use of all these groups which will allow the efficient sharingof ideas and designs.

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2 Medium Energy Electronuclear Physics

Proton Electromagnetic Form Factor at Low Q2

Since the proton magnetic moment differs from that of a structureless Dirac particle

µ 6= q

mc|~s|, (1)

where µ, q, m, and s are the magnetic moment, electric charge, mass and spin of theparticle, respectively, and c is the speed of light, these particles must have an internalstructure. Electron scattering experiments were used starting in the 1950s to unravel thedistributions of electric charge and magnetization in the nucleons. The elastic scatteringcross section is given by a product of the scattering cross section from a point-like particle,multiplied by form factors that contain the information about the internal structure ofthe nucleons:

dσ

dΩ=α2

Q2

(E ′

E

)2cot2 θe

2

1 + τ

[G2E + τ

(1 + 2(1 + τ) tan2 θe

2

)G2M

]= σMott

[G2E +

τ

εG2M

](2)

Here α is the electromagnetic coupling constant, Q2 is the four-momentum transfer, Eand E ′ are the electron incoming and outgoing energies, θe is the electron scattering angle,τ = Q2/4mp, and GE and GM , which depend on Q2, are the electric and magnetic formfactors, σMott is the Mott cross section for electron scattering from a point–like particle andε is the virtual photon polarization. The form factors have usually been determined with a“Rosenbluth Separation” [1], in which the eN elastic cross section is measured at differentbeam energies and angles, corresponding to different ε values but the same momentumtransfer. In non-relativistic quantum mechanics, the charge and magnetization spacialdistributions are connected to the form factors through a Fourier transform; in relativisticquantum mechanics, understanding the spacial distributions is problematic, as they aremodel dependent.

The nucleon form factors (except for GnE which must go to zero as Q2 → 0) were found

to approximately follow the dipole form factor formula,

GD =

(1 +

Q2

λ2D

)−2

,

where λ2D ≈ 0.71 GeV2 is an empirical parameter found to be identical for the three form

factors GpE, Gp

M , and GnM , so that Gp

E ≈ GD, and Gp,nM ≈ µp,nGD. The dipole form factor

corresponds to an exponential charge and magnetization distribution, which would resultfrom a δ-function potential. In so far as the nucleon is small, this observation makes someintuitive sense. Since in the dipole approximation all form factors are equal except for anoverall scale, it is evident that the ratio of the proton electric to magnetic form factors(multiplied by the proton magnetic moment) should be equal to one.

Starting in the late 1960’s and early 1970’s, experiments started to observe deviations from

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the simple dipole formulas for the form factors. For example, Berger et al. [2] observeddeviations at the level of a few tens of percent at high Q2, 1 GeV2 or so, for Gp

E andGpM . But these measurements were not very precise, and more precise recent cross section

measurements from SLAC [3,4] and Jefferson Lab [5,6] indicate better agreement, to withinabout 10%, with the dipole formula at high Q2. Some of the recent data, for the formfactor ratio, are shown in Figure 1, taken from [6]. In the 1970’s and 1980’s, more precisecross section measurements on the proton [7,8] at low Q2 also observed deviations fromthe dipole formulas of a few percent at low Q2, but these observations appear to have hadlittle impact, with interest in form factors largely focused on high Q2 and Gn

E.

Fig. 1. Data on the proton Electric to Magnetic Form Factor Ratio, including the olderRosenbluth separation data (crosses) from a global reanalysi s [9], newer polarization trans-fer data [10–12] (triangles) and the most recent JLab Rosenbluth separation data [6] (filledcircles).

For the past decade, most new form factor measurements have relied on polarizationtechniques. The Recoil Polarization method [13–15] has been used by most recent mea-surements [10–12,16,17] to extract the proton form factor ratio, whereas polarized beam– polarized target asymmetries have been more common for neutron form factor measure-ments. The proton form factor ratio is calculated from the ratio of transferred polarizationcomponents of the recoil proton:

GE

GM

= −PxPz

E + E ′

2Mp

tanθe2. (3)

Here Px and Pz are the transferred polarization components,

σredPx =−2√τ(1 + τ) tan

θe2GEGM , and (4)

σredPz =E + E ′

Mp

√τ(1 + τ) tan2 θe

2G2M . (5)

4

where σred is the reduced cross section.

The recoil polarization form factor measurements show a strong deviation at high Q2 fromthe expected ratio of one [10,12,17]; see Figure 1. It is now generally accepted theoreti-cally that two-photon exchange corrections account for much, if not all, of the differencesbetween the Rosenbluth and polarization transfer techniques – see [18–22]. It is believedthat these corrections have little impact on the polarization technique for determiningform factors, but have large impact on the Rosenbluth technique, as both two-photon cor-rections and the electric form factor typically contribute a few percent of the cross sectionat high Q2. Such corrections have been cleanly demonstrated in low Q2 transverse beamasymmetries in parity-violation measurements [23,24], but not in high Q2 form factormeasurements; several such experiments have been approved by the Jefferson Lab PACand are awaiting beam time.

Recent measurements in Hall A [25] have demonstrated the recoil polarization method tobe effective at low Q2. These measurement have also conclusively shown a deviation ofthe FF ratio from unity, even at low Q2, and have managed to attribute the deviation toa reduction of the electric form factor with respect to standard parametrizations. How-ever, these measurements were taken in a short time with low beam polarization. A highprecision experiment, E08007 [26], to measure the proton form factor ratio was proposedand approved for JLab Hall A. Preliminary results from the first part of the experiment,which used recoil polarization, are shown in Fig. 2 and confirm the results from [25].

Fig. 2. Preliminary results from part I of E08-007 (red circles) and E03-104 (blue circle) . Alsoshown are Rosenbluth measurements (light green ) and older polarization measurements. Theresults show a strong deviation of the form factor ratio from unity, even at low Q2 and noevidence of suggested narrow structures.

Despite the above, the recoil polarization method has some drawbacks when consideringa very low Q2 measurement. First, the method of recoil polarization relies on a secondary

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scattering which takes place in a (usually) carbon analyzer. When performing a low-Q2

measurements, the recoil proton is ejected with too low a momentum to be detected inthe rear drift chambers. Second, due to the low energy of the ejected proton it loses asignificant fraction of its momentum in traversing the target cell, rendering an accuratemeasurement difficult owing to the need to take into account the energy loss due tomultiple scattering. And last, the energy of the recoil proton favors an elastic secondaryscattering with the carbon nuclei in the analyzer, a process resulting in a larger analyzingpower for large scattering angles, resulting in a reduction of the figure of merit of thepolarimeter in the acceptance range of the Hall A FPP.

An alternative method is to use beam-target asymmetry, where a polarized beam is scat-tered off a polarized target. For elastic scattering of polarized electrons off polarized pro-tons the cross section difference between helicity states is:

1

2

[σ+ − σ−

]=−2σMott

E ′

E

√τ

1 + τtan

θe2

√√√√τ (1 + (1 + τ) tan2 θe

2

)cos θ∗G2

M

+ sin θ∗ cosφ∗GMGE

. (6)

Where θe, σMott, E, E ′ are the same as in Eq. (2), and θ∗ (φ∗) is the target spin polar(azimuthal) angle.The asymmetry is then:

A≡ σ+ − σ−(σ+ + σ−)PbPt f

(7)

=−2√

τ1+τ

tan θ2

√τ(1 + (1 + τ) tan2 θ

2

)cosθ∗G2

M + sin θ∗ cosφ∗GMGE

(PbPt f)

(G2

e+τG2M

1+τ+ 2τG2

M tan2(θ/2)) ,

where Pb(Pt) are the beam (target) polarization and and f is the dilution factor whichreduces the amount of hydrogen seen by the beam due to the fact that the target, beingcomposed of 15NH3 also contains nitrogen atoms.

We have designed a novel technique, utilizing the two identical detectors in JLab Hall A,which greatly reduces systematic effects in the measurement. By taking the ratio of asym-metries measured in two identical spectrometers almost all of the systematic uncertaintiesare canceled and very high precision may be achieved down to low Q2.

Figure 3 shows the coordinate system for the reaction ~p(~e, e′)p. Figure 4 shows the kine-matics for the two simultaneous measurements.

We may then invert the ratio of the asymmetries to obtain the equation

µPGPE

GPM

= −µPa(τ, θ) cos θ∗1 − f2

f1Γa(τ, θ) cos θ∗2

cosφ∗1 sin θ∗1 − f2f1

Γ cosφ∗2 sin θ∗2(8)

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Fig. 3. Coordinate system for the reaction ~p(~e, e′)p.

Fig. 4. The kinematics for the two simultaneous measurement. The scattered electrons e′1 and e′2are detected in HRSRight and HRSLeft respectively. The protons p1 and p2 recoil in the directionof the q-vectors ~q1 and ~q2 repectively. ~S denotes the target spin polarization vector.

Where a(τ, θ) =√τ(1 + (1 + τ) tan2(θe/2)), θ∗i (φ

∗i ) are the polar (azimuthal) angle of the

target spin with respect to the ~q in the ith spectrometer, and Γ = A1

A2is the ratio of the

asymmetries between the two spectrometers (note that Pb, Pt and f cancel out whentaking the ratio).

The projected uncertainties from the second part of the experiment are shown in Fig. 5.

The results from the experiment have a profound impact on many areas of nuclear andatomic physics, for example, the calculation of the hydrogen hyperfine splitting relies onthe Zemach radius [27,28] which encodes the spatial information about the deviation ofthe proton from a point particle. These calculations rely on an accurate knowledge of theproton form factors (particularly at low Q2).

We have also shown [29] that measurements of the form factor ratio at low Q2 indicate that

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Fig. 5. Projected uncertainties for part II of E08-007 (magneta), the other symbols are the sameas in Fig. 2. Lines show several theoretical calculations and fits.

the proton transverse RMS magnetization radius extends further than the RMS chargeradius. For a discussion of the impacts of these measurements see [30] and referencestherein.

Part II of E08007 has been scheduled to run during January 2012, significant prepara-tory work must still be done before the experiment. The polarized NH3 target must beoptimized for use in JLab Hall A, the Hall A beamline must be modified to account forelectron beam deflections in the (strong) target field, and the hall A detector must beconfigured with (new) septum magnets to allow for small angle electron detection. Like-wise, simulation and analysis code must be written to modify the hall A standard analysispackages.

Another experimental group is scheduled to run in tandem with E08007 part II using anidentical setup. A collaboration with that group has been initiated in order to promote aconcentrated effort in preparation for the experiments. It is expected that the TAU groupwill be intimately involved in preparation for the experiment and in the analysis of theE08007-II results. There is much knowledge and experience to be gained in this endeavor,particularly as regards to the polarized target setup, which has never been experimentallyused by a group from Israel. It likely that at least one PhD and one MSc student fromTAU may take part in this experimental effort.

Nucleon Structure Modification in the Nuclear Medium

That the nucleon properties are modified in the nuclear medium in an incontrovertiblefact, a (somewhat trivial) example of this is the change of the neutron lifetime, fromapproximately 15 min for a free neutron, to infinity for a nucleon bound in a stable

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nucleus. Further, more compelling evidence was shown in 1983 in a reduction of the F2

structure function in iron vs. deuterium [31], this has come to be known as the EMC effectand has since been confirmed experimentally for both heavy [32–36] and light [37] nuclei.For a reviews of the EMC effect see [38,39] and references therein.

Modification of the nucleon in the medium has also been suggested in other observables,such as, for example, the quenching of the axial form factor [40], and quenching of theCoulomb Sum Rule (CSR) [41].

Generally speaking, two classes of explanations have been proposed for the observed ef-fects:

• Nuclear structure effects - In which the observed effect is deemed to originate fromthe nuclear medium, i.e. non-nucleonic degrees of freedom, while the nucleons are un-changed. One example is the incorporation of the enhancement of the anti-quark pop-ulation in the nucleon due to the exchange of quark-anti qurak pairs [42–45].• Nucleon structure modification - In which the fundamental structure of the nucleon

is modified. An example of such models are dynamical rescaling models (for exam-ple [46–48]) in which the quark confinement scale of a quark in the nucleus is modified.Such changes are sometimes interpreted as the ”swelling” of the nucleus in the nuclearmedium, namely, an increase in the electric or magnetic radii of the bound nucleus (orboth).

While the suggested models have explained some of the observed effects, none of themodels has managed to completely explain all the observations. Furthermore, several ofthe effects (most notably the EMC effects) may be explained by the application of widelydifferent models.

In an effort to help determine the origin of these effects several authors have suggested [49–51] to perform measurements of the polarization components of a nucleon knocked outfrom a nucleus by a polarized electron beam, and compare to the components of a freenucleon. These calculations have shown that the nuclear effects (such as Meson ExchangeCurrents) are minimized in the measurement of the polarization components. These sug-gestions were developed into an experimental program at the MAMI facility at Mainz [52]and the JLab facility [52,53] in which the ratio of the transverse to longitudinal compo-nents of a proton knocked out from 4He (4He(~e, v′~p)3H) was compared to that of a freeproton (H(~e, e′~p)) by the extraction of a super-ratio:

R =(Px/Py)4He

(Px/Py)H(9)

Fig. 6 shows the extracted super-ratio. The figure clearly shows a reduction in the po-larization ratio for a bound nucleon, consistent with models incorporating a modificationof the nucleon structure [54,55]. It is worth noting that Schiavilla et al. [56] have shownthat the effect may also be attributed to strong, spin-dependent, final state interactions,although measurement of the induced polarization seem to rule out this explanation [53].

In a recent paper [57] we have shown, that using several different models for the nucleon

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Fig. 6. The super-ratio of polarization components of a bound proton to a free one.

modification in the medium, the polarization component ratio for the neutron is enhancedrelative to the free neutron (as opposed to the quenching observed and calculated for theproton). Fig. 7, taken from [57], shows the results of our calculations of the form factorsuper ratio for the neutron and the proton.

Fig. 7. The calculated form factor super-ratio for neutrons and protons in 4He using two theo-retical models.

The prediction for the neutron polarization component ratio has led us to consider an

10

experimental proposal which will measure this effect. This proposal is currently underdevelopment and will be submitted to the JLab PAC in January 2010, another possiblevenue for this experiment (also currently under investigation) is the A1 electron scatteringhall at the Mainz MAMI facility.

In order to perform the experiment a new neutron polarimeter must be designed, tested,and constructed. Unlike the neutron polarimeter previously used for Gn

E measurementat JLab [58], which only measured the transverse polarization components, the new po-larimeter must be able to measure the normal (induced) polarization component in orderto detect possible final state interaction effects (a la Schiavilla et al. [56]). The TAU groupwill take an active part in the design, test, optimization and construction of the neutronpolarimeter

Several theoretical challenges must be overcome in order to achieve the desired precisionin the results:

• Unlike the case for the proton, comparison of the bound neutron results will have tobe performed with the results from a neutron bound in a deuteron. This requires anaccurate theoretical calculation for the deuteron in order to disentangle any existingbinding effects.• The limited energy resolution achievable for the recoil neutron will limit the missing

mass resolution of the final state (in effect, the degree to which the final state can beknown to be e′+n+ 3He). The theoretical calculation the result is to be compared withmust take into account the possible mixing of the final states (this problem is somewhatsimplified due to the lack of excited states in 3He).• Since the cross section for ep scattering is significantly larger than the cross section foren scattering, significant final state interactions may be present (in which the electron isscattered off a proton, which is then scattered off a neutron, mimicking en scattering).

These challenges must be dealt with in the theoretical analysis of the experiment sincethey cannot be eliminated experimentally (note that the design of the experiment willincorporate input from theory as to kinematics which may minimize some of these ef-fects). Several leading theoretical groups have expressed desire to collaborate with theexperimental group in these efforts. Among these groups are the University of Washing-ton group (G. A. Miller et al.), and, most notably, Prof. Nir Barnea’s Hebrew Universitygroup (Prof. Barnea has already tasked a Ph.D. student to these calculations).

3 Standard Model Tests with Rare Nuclei

The standard model of particle physics (SM) [59] is currently the best theory we havefor describing the myriad interactions existing in nature. However, the standard model islacking is several crucial details, among which are (for example):

• Gravity is not currently included in the SM.• It does not explain the matter-antimatter asymmetry in the universe.• It has a plethora of arbitrary parameters which must be tuned by experimental results.

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Thus, there is evidence that there exists physics beyond the standard model, promptingmany new theoretical attempts to describe such physics (string and SUSY theories, toname but a few).

Experiments testing for beyond SM physics must either test at energy regimes which haveso far not been accessible (such is the case with, for example, the LHC) or test at lowerenergies but with extremely high precision (to allow for detection of the tiny deviationsfrom the standard model which may be caused by the new physics).

Such low energy experiments cannot make use of the strong interaction since due toconfinement effects our ability to compare the experiment to theory is severely limited.Thus, such experiment are inevitably led to test the SM using ElectroWeak interactions,for which the theoretical calculations may be precisely performed.

In general, these experimental efforts may be classed according to several general groups:electron scattering experiments (example, the JLab QWeak [60] experiment), neutrinoscattering experiments (LSND [61], NuTev [62] and the like), atomic parity-violationexperiment (eg, the 133Cs [63] and the Berkeley Yb [64] experiments), and beta-decayexperiments, which are the topic of this research proposal.

In the standard model description of the electroweak interaction the photon has heavy,spin-1 partners, the Z0,W± bosons which mediate the weak interaction. Due to the largemass and vector nature of these bosons the Lorentz transformation properties of the ef-fective low energy four-Fermion contact interaction operators are vector and axial vector.Phenomenologically, the weak interaction is completely chiral: coupling only left-handedneutrinos and maximally violating parity. However, there is no ab-initio reason for theseproperties of the weak interaction, and beyond SM theories may (and have been) con-structed in which a small deviation from these properties is introduced (for example, bythe inclusion of right handed currents).

At the low momentum transfers of β decay (in the SM or any extension based on theexchange of massive bosons), the β decay hamiltonian reduces to a sum of 4-Fermioncontact interactions:

Hint =∑X

(ψpOXψn

) (CXψeOXψν + C ′XψeOXγ

5ψν)

(10)

where OX denotes operators with the different possible Lorenz transformation propertiesvector (V), axial vector (A), tensor (T), scalar (S), and pseudoscalar (P), and implicitlyincludes all contracted 4-indices (in fact, the pseudoscalar term does not contribute to(the non-relativistic) β decay since it couples the ”large” and ”small” components of thewavefunction. For a complete review of β decay formalism see refs. [65,66]. In the SM, theinteraction between the quarks and the leptons is of the type ’V-A’, giving CV = C ′V andCA = −C ′A and emitting only left handed neutrinos.

The value of CA is renormalized by the strong interaction between the quarks to≈1.26, butthe interaction still only gives rise to left handed couplings. Similarly, in the SM, all othercoupling coefficients are identically zero in the quark-lepton interaction but may becomeallowed in the nucleon-lepton interactions, these are termed ”induced currents and are

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groups into ”allowed” (G-parity invariant) or ”first-class” and ”second-class” (G-parityviolating) currents (see [67]).

The most general expression for the nuclear β decay rate, Γ, in terms of the angularorientations and distributions of the leptons, including spin polarization of the nucleus, isgiven by [68]:

ΓdEedΩedΩν =F (±Z,Ee)

(2π)5peEe(E0 − Ee)2dEedΩedΩν

ξ

2×1 + aβν

~pe · ~pνEeEν

+ bme

Ee+ c

(1

3

~pe · ~pνEeEν

− ~pe · iEeEν

)I(I + 1)− 3⟨(~i · i)2

⟩I(2I − 1)

+

⟨~I⟩I·(Aβ

~peEe

+Bν~pνEν

+D~pe × ~pνEeEν

) , (11)

where F is the Fermi function, ~p and E and the lepton momenta and energies, I and iare the nuclear spin polarization and direction,

ξ = |MF |2(|CV |2 + |C ′V |

2+ |CS|2 + |C ′S|

2)

+ |MGT |2(|CA|2 + |C ′A|

2+ |CT |2 + |C ′T |

2),

and MF and MGT are the Fermi and Gamow-Teller matrix element of the beta decay.

The correlation coefficients are given explicitly in [68], for example, aβν , the electron-neutrino correlation coefficient is given by

aβν =[|MF |2

(|CV |2 + |C ′V |

2 − |CS|2 − |C ′S|2)− 1

3|MGT |2

(|CA|2 + |C ′A|

2 − |CT |2 − |C ′T |2)]ξ−1,

(12)

clearly, a deviation from the standard model prediction of aβν is an indication for theexistence of scalar or tensor currents. Tests of aβν for different isotopes (with differentvalue of MF and MGF ) probe different possible linear combinations of tensor and scalarcontributions (for example, the superallowed 0+ → 0+ decays are a probe for scalarinteractions, since for these decays MGT = 0, the standard model prediction for thesuperallowed decays is aSMβν = 1).

Table 1 summarized the observables and sensitivities physics to new physics of the corre-lations coefficients in Eq. 11.

Magneto-Optical Trapping of Rare Atoms

Magneto-optical trapping of neutral atoms is achieved by damping provided from retrore-flected laser light from three orthogonal directions, detuned a few linewidths to the redof the atomic transition (Fig. 8). Atoms moving in any direction see light opposing theirmotion Doppler shifted closer to resonance, and preferentially absorb that light and slow

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Coefficient Observable Sensitivity SM Predictionaβν β − ν correlation Tensor and Scalar inter-

actions1(pure F), −1

3 (pureGT) or combination

b Energy dependence ofother coefficients

SV and TA interference 0

Aβ β asymmetry for polar-ized nuclei

Tensor terms, ST/VAinterference, parity vio-lation

nucleus dependent

Bν ν asymmetry for polar-ized nuclei

Tensor terms,TA/ST/VA/SA/VTinterference, parityviolation

nucleus dependent

D Triple product ST/VA interference,time reversal invariance

0

Table 1Observables, physics sensitivities and SM predictions for the β decay rate correlation coefficients.

down by spontaneous emission. A linear restoring force is provided by a weak magneticquadrupole field with a gradient of O(10 G/cm) produced by anti-Helmholtz coils. Themagnetic field changes sign at the origin, changing the sing of the Zeeman splitting andthus the probability of absorbing circularly polarized light with opposite handedness inthe opposing beams (See Fig. 9). Coupled with the red detuned laser beams this createsa dissipative trap which cools and confines the atoms. The MOT may be thought of as anoverdamped harmonic oscillator, with a cloud of atoms ∼ 1 mm in diameter collected atthe origin. Due to the near-resonant light, MOTs are inherently isotope (and even isomer)selective. The mean lifetime of the MOT is limited by the average collision cross-sectionwith residual gas, requiring a high vacuum to operate efficiently. For an overview of opticaltrapping of atoms see [69].

The experimental properties of the MOT make it an ideal device for measuring the weakdecay of trapped rare atoms. The low energy nuclear recoil from β decay escape theMOT, they are no longer resonant with the laser light and the magnetic field is too smallto confine them. Using a simple detector setup it is possible to detect the recoil nuclei, theemitted β particles, and the shakeoff electrons. A complete reconstruction of the reactionmay then be performed and the correlation coefficients extracted (in fact, one must usuallyuse a Monte Carlo simulation in order to extract the correlation coefficients).

The most commonly trapped atoms are the alkali atoms, which have a simple electronictransition scheme, at accessible laser wavelengths, which can be easily used to trap theatoms. Most notably the Berkeley group has trapped 21Na[70,71] (an improved measure-ment is currently underway) and the TRIUMF group has trapped 38mK[72]. Several groupshave also trapped rare alkali elements and studied their β decay properties.

Other atomic species may be trapped by careful selection of the trapping wavelengths.Particularly of interest to the study of β decay are the noble gases, which must be trappedin the metastable state (see Sec. 4). While no experiment has yet measured the correlationcoefficients using a MOT, results have been published using distributed sources (see foreg. [73]).

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Fig. 8. Schematic of a 3D Magneto-Optical trap. Three orthogonal retroreflected slow the atomswhile coils with opposing currents provide the linear restoring force.

Fig. 9. Simple 1D MOT model for an atom with J=0 ground state and J=1 excited state.

The ANL group has recently demonstrated the optical trapping of 6He [74] and is currentlydesigning an experiment to measure aβν in the pure Gammow-Teller decay 6He → 6Li.We have initiated a collaboration with the ANL group to utilize the ANL 6He trap for ameasurement of the beta decay coefficients. As a first stage the trap will be rebuilt andtested at the Argonne ATLAS facility. The trap will than be moved for additional testingin the CENPA facilities at the University of Washington in Seattle and will finally bedeployed for the measurement at the SARAF facility in Israel.

This research will focus on the trapping 19Ne isotope (with a possible later extension to18Ne). The properties of 19Ne are listed in Tab. 2.

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Lifetime ∼ 17.5 secDecay scheme 1

2

+ → 12

+ 99.9986%12

+ → 12

− (110keV) 1.2 · 10−2%Table 219Ne properties.

19Ne is an interesting isotope for study, in that several measurements may be performedto test the standard model. I propose to perform the following measurements:

• A measurement of the beta-neutrino correlation coefficient aβν .• A measurements of the beta asymmetry parameter Aβ using a polarized trap.• A measurements of the ν asymmetry parameter Bβ using a polarized trap (by detection

of the recoil ion).• A time reversal invariance test, using a measurement of the D coefficient in a polarized

trap.• Extraction of the Vud CKM matrix element using Aβ and aβν (see [75]).

It is noteworthy that measurements using 18Ne, tagging on the γ ray from the differentfinal states, enable simultaneous measurements of both pure Fermi and pure Gammow-Teller decays (see Fig. 10).

Fig. 10. 18Ne decay scheme. Decay into the excited state of 18F is pure Fermi while decay intothe ground state is pure Gammow-Teller.

Some of the above measurements require the population of the trapped atoms to bepolarized. Polarizing the atoms requires the application of a magnetic field to induceZeeman splitting of the ground state, and the absorption of circularly polarized laser lighton the atoms (several absorption/emission cycles per atom). Thus, polarizing the atomscannot be performed while the atoms are trapped by the MOT. Polarizing the trappedatoms is done by releasing the (anti-Helmholtz) trapping field and the tapping laser beamsand applying a magnetic field using Helmholtz coils (usually the same coils used trappingwith the currents, now in series). This scheme requires the field to be rapidly switchedfrom trapping to polarizing in order for the atoms to be polarized before a significantfraction is lost to ballistic expansion. A rapid reversal of the field, however, causes eddycurrents in the system which induce a delay between the field switching and the usefulmeasurement time. This research will investigate methods to reduce the time required

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between the trapping and polarized phases. Several possible schemes will be investigated:

• Cycling schemes, in which the system will alternate between trapping and measuring.The duty factor used will determine the useful measurement time. Two possible methodsare:· By using a combination of clamp diodes in series with the coils and slits in the metal

components of the system (for example in the accelerating electrodes) it is possibleto reduce the eddy currents induced in the system.· In Ref [76], a method was demonstrated, in which an alternating current trapping

field was used (in combination with alternating trapping beam polarizations). Thefield may then be turned off at the zero crossing point, eliminating eddy currents.This method is currently under investigation at LBL for use with the Berkeley 21Na,should it prove to be effective it may be adapted for use with a Ne trap.

• Dark, all optical, traps: In these schemes the atoms are loaded from the MOT intoa dark, all optical, far blue-detuned trap (see Ref [77] and references therein). Sincethe trapping is now non magnetic the MOT field may be slowly ramped down andswitched to a polarizing field without losing the trapped atoms, in these schemes theduty factor is theoretically 100% since the MOT is completely turned off, the limitingfactor, however, is now the loading efficiency of the optical trap. Two such trap designswill be investigated:· In Ref [78] a single beam optical was demonstrated using two axicon lens and a

diffractive element. Such a trap has relatively large volume and can potentially beefficiently loaded from the MOT. While trapping atoms in such a trap has not beenyet experimentally demonstrated, such a trap geometry has been shown. Modificationof this design will be performed for a neon trap and the loading efficiency and lifetimewill be investigated.· In [79,80] a scanning beam trap was demonstrated, in which a rotating, blue detuned,

laser beam formed a dynamical optical trap. While these traps have typically a smallervolume, a great advantage is the possibility of dynamically modifying the trap geom-etry and dimensions by changing the scanning parameters. We will investigate theapplicability of such a trap for neon isotopes and optimize for efficient loading (alarge initial trap) and high final densities and precise position determination (a smallfinal trap) by adiabatically reducing the trap size.

The neon trap research will be performed in collaboration with the weak interactionsgroup at the Lawrence Berkeley Lab and UC Berkeley. Construction of the neon trapwill commence at LBL and will later be transferred to the Tel Aviv University, it isexpected that testing the different trapping schemes, optimizing the trap setup and thedata analysis will be a joint effort between the two experimental groups (with studentsfrom LBL spending time at TAU and vice-versa).

The actual experiment will be conducted at either the LBL 88” cyclotron facility or theSARAF experimental facility, depending on beam availably and the production efficiencyfor the different isotopes (it is likely, for example, that 18Ne will not be produced atSARAF, experiments on that isotope will most likely be conducted at LBL.)

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Electrostatic Traps for Rare Ions

While optical traps have many advantages for weak interaction studies a serious dis-advantage is the limited range of isotopes which may be trapped (due to the limitedavailability of laser sources). Several experiments have measured the beta decay of rareisotopes trapped in a magnetic trap (see for example [81]). Such traps have the advantagethat they can potentially trap almost any isotope. These traps, however, utilize a strongmagnetic field for the trapping potential and, like a MOT, is limited in efficiency by thesolid angle occupied by the detector.

An alternative ion trapping scheme in presented in [82,83], a moving bunched ion beam istrapped in a completely electrostatic trap. Such a trap has long been used (for example,at the Weizmann institute and at Heidelberg) for experiments on trapped molecular ions.We propose to use this trap design to measure the beta decay of a rare ion beam injectedinto the trap. Due to the nature of the trap, most of the trap volume is completelyfield free, with the electrostatic field existing only at the the trap ends (the electrostaticmirrors). This enables the detection of the the decay products in the field free region bysurrounding the moving ion beam with beta particle detectors. Detection of the recoil ionsmay be performed by placing microchannel plates (with circular holes drilled in them forthe through beam) in front of the electrostatic mirrors. Due to the large kinetic energyof the beam the recoil ions are kinematically focused on the MCP and arrive with highkinetic energy, removing the need for electrostatic acceleration prior to detection (as isneeded in MOTs and magnetic traps).

By employing an axial magnetic field (which does not interfere with the ion beam since itis collinear to it) and a collinear laser beam, the moving ions may be polarized to enablemeasurements of the polarization dependent correlation coefficients. By using two, dopplerdetuned, laser beams two separate polarization populations may be created (parallel andanti-parallel to the magnetic field) to enable an asymmetry measurement using a singlefield setting.

A schematic illustration of the trap setup is shown is Fig. 11.

Fig. 11. Schematic illustration of a possible measurement scheme using an electrostatic trap.

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Simulations have shown that the detection efficiency of such a trap setup is over 50%,thus, using even a small population of trapped ions, high statistical precision may beachieved.

Such a trap may also easily be modified to trap different species of rare ions. Since calcu-lation of the SM coefficients is not possible to high accuracy for all isotopes (namely, it isvery hard for isotopes far from N=Z and far from stability) the logic of the measurementmay be inverted. By measuring the correlation coefficients and assuming the SM it ispossible to extract linear combinations of the Gammow-Teller and Fermi matrix elementsand test them against theoretical calculations (for example shell-model or GFMC calcu-lations). Taking advantage of the high detection efficiency, even longer lived species maybe examined.

Such a trap design is currently under investigation in collaboration with the WeizmannInstitute nuclear physics and electrostatic trap groups. There are also plans for the con-struction or acquisition of such a trap at LBL, which will also be used for isotope massmeasurements. While the construction of such a trap is not currently planned for thisproposal at TAU, collaboration with the WI and LBL groups will continue and an activepart in the design, construction and utilization of this trap setup is envisioned (with TAUstudents taking a leading role in these experiments).

4 All Optical Excitation of Metastable Noble Gases

A serious disadvantage of performing experiments with optically trapped noble gasesderives from the closed shell structure of these gases. Namely, there are, at present, noavailable lasers with the extremely short wavelength needed (for example, trapping groundstate neon would require a wavelength of ≈74 nm).

Thus, these gases must be trapped in the (long lived) metastable state which behaves inmuch the same way as an alkali gas. The metastable state is typically reached by RF orDC excitation of the gas, in which the atoms are singly ionized and the free electron isrecaptured into the metastable state. Unfortunately, the efficiency for such a process is onthe order of 10−5 – 10−6. The low efficiency presents less of a problem when trapping thestable isotopes, but does, however, severely limit the achievable statistics when performingbeta decay measurements of the rare isotopes, which are produced is small numbers.

An alternate method, developed at Argonne National Lab for Krypton isotopes [84,85],relies on all optical excitation using three optical transitions was able to achieve an en-hancement of two orders of magnitude of the efficiency.

This part of the research will focus on modifying the ANL method to allow for all opticalexcitation of Neon and Argon isotopes. Initially the research will demonstrate the excita-tion of the stable and long lived isotopes. The second stage of the research will use the rareNeon and Argon isotopes which will be produced at the SARAF and other facilities (e.g.,LBL) and demonstrate all optical excitation of these isotopes, allowing for an increase inthe number of rare atoms which may be trapped in the magneto-optical trap.

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5 The SARAF Connection

Due to the short lifetime of atom and ions traps (caused mostly by collisions with residualgas) only species with relatively short lifetimes will produce adequate statistics. Thus, thetrapped species must be produced online in accelerator facilities and trapped, necessitatingthe installation of the experimental setup at a research facility capable of producing theradioactive element for trapping.

An interesting development in that area is the planned Soreq Applied Research Accel-erator Facility (SARAF), a 40MeV proton and deuteron accelerator, under constructionat the Soreq Research Center in Israel [86]. While the relatively low energy of SARAFwill preclude the production of isotopes far from stability (since, for example, spallationreactions are mostly not possible there) the high (5mA) beam current will enable theproduction of copious amounts of light radioactive nuclei. For example, calculations showthat using an (n, α) production scheme (with the neutrons coming from a liquid lithiumprimary target) on BeO it will be possible to produce 8Li at a rate of 1012 atoms/sec. Itis also likely that a production scheme may be designed to enable a high volume produc-tion of 19Ne (and potentially 18Ne). Production schemes for 8Li and 6He are now underinvestigation by the Weizmann Institute group.

The advantage of a Israeli based production facility for trapping experiments is obvious.A rapid R&D cycle can be sustained between offline development at (for example) TAUand online deployment of the experimental setup at SARAF.

It is also worthwhile to note that although the facility is expected to be fully operationalin 2014, phase I of the project (to be completed sooner) will already make available a5MeV, high-current beam, also usable for a lower volume production of rare isotopes.

It is expected that this research will make use of the SARAF facility and influence thedesigns of the target area and planned production schemes. Though production of rareisotopes is in itself a complex and rich research subject it is expected that researchers andstudents involved in the trapping experiments will play an active part in the design andtesting of the production mechanism of the relevant isotopes at SARAF.

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